Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

Let $S$ denote the functions that are analytic and univalent in the open unit disk and satisfy $f(0) = 0$ and $f\prime(0) = 1$. Also, let $K, St, S_R$, and $C$ be the ...

Financial executive pay is a convex function of profits if recipients get a greater increment in pay when returns are high as opposed to moderate, compared with when returns are moderate as opposed to ...